ContentMultiple zeta values are real numbers appearing in several areas of mathematics and theoretical physics. These numbers are natural generalizations of special values of the Riemann zeta function. They have been studied at least since Euler, who found many of their algebraic properties. Having been seemingly forgotten for more than 200 years, multiple zeta values were rediscovered by many mathematicians and theoretical physicists since the 1980s in several different contexts (modular forms, mixed Tate motives, quantum groups, moduli spaces of vector bundles, scattering amplitudes, resurgence theory, etc.). (See the textbooks/lecture notes [AK], [BF], [W] and [Z])

​The goal of this course is to give an introduction to the theory of multiple zeta values and to explain their connection to modular forms as given in [GKZ] and [B2]. For this, we will cover roughly the following topics

The Riemann zeta-function and its special values ([AK], ​[BF], [W], [Z])

​Lecture schedule: ​Each week we will have a Zoom meeting at Friday 16:00-17:00 (Tokyo time) to discuss the current materials & exercises. The meetings ID and password are available in the NUCT course page. If you are not in the NUCT course and you want to join these meetings please write me an email.

If you want to get credits for this course I expect you to join the Zoom lectures each Friday.

The grading will be based on written homework assignments. During the course, we will provide Exercises (at the end of the lecture notes), which you need to hand in until August 9th, 2020.

It is not decided yet how many Exercises there will be, but the idea is to give roughly 1-2 Exercises each week, which can be found at the end of the lecture notes or above.

Please feel free to hand in Exercises separately before the deadline to get feedback as early as possible. (i.e. after finishing one Exercise please feel free to send it directly instead of sending the solutions of all exercises at once on August 9th)